The study of area-minimizing surfaces goes back to Euler and Lagrange. It was Euler who discovered the first non-planar area-minimizing surface (about 1745), and it was Lagrange (about 1760) who discovered the equation that is satisfied by any smooth function with an area-minimizing graph. I will sketch how the mathematical consequences of area-minimization arise. It is remarkable that many solutions of the resulting equations can be written down, and computer graphics make it possible to visualize those surfaces. I think the number of pictures will exceed the number of equations.